Question: Abe is going to plant $54$ oak trees and $27$ pine trees. Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Abe can have in each row?
Solution: In order to know how many trees Abe can have in each row, we need a number that is a factor of ${54}$ and ${27}$, so that the ${54}$ oak trees and the ${27}$ pine trees can be divided up into equal rows. So, if each row had $\gray{9}$ trees, there would be ${54} \div \gray{9} = 6$ rows of oak trees and ${27} \div \gray{9} = 3$ rows of pine trees. This creates equal rows, but it isn't the greatest number of trees per row! To find the greatest number of trees, we want to find the greatest common factor of ${54}$ and ${27}$. To do so, let's find factors of ${54}$ and ${27}$. ${54}$ : $1, 2, 3, 6, 9, 18, {27}, 54$ ${27}$ : $1, 3, 9, {27}$ The greatest common factor of ${54}$ and ${27}$ is ${27}$. In math notation this looks like: $ \text{gcf}({54}, {27}) = {27}$. The greatest number of trees that Abe can have in each row is ${27}$.